** Next:** Numerical examples
** Up:** Shan and Biondi: Plane-wave
** Previous:** Introduction

Plane-wave (source plane-wave) migration
Duquet et al. (2001); Liu et al. (2002); Rietveld (1995); Whitmore (1995); Zhang et al. (2005)
synthesizes plane-wave source experiments from shot records. The recorded data are
decomposed into plane source gathers by slant-stack processing:
| |
(1) |

where *x*_{s} is the source location, *x*_{r} is the receiver location, *p* is the ray parameter,
*U* is the recorded surface data, and *u* is the synthesized surface data for the plane-wave source. The corresponding
plane-source is
| |
(2) |

The plane-wave source *d* and its corresponding synthesized data *u* are independently extrapolated into the
subsurface, and the image can be obtained by cross-correlating these two wavefields.
Plane-wave migration is potentially more efficient than shot-profile migration.
It uses the whole seismic survey as the migration aperture, which is helpful for imaging
steeply dipping reflectors.
**bpvelall
**

Figure 2 The velocity model.

Given the plane-wave source with a ray-parameter *p*, its take-off angle at the surface is , where *v* is the surface velocity.
we use tilted coordinates satisfying

| |
(3) |

where (*x*,*z*) are Cartesian coordinates and is an angle close to the take-off angle of the plane-wave
source at the surface.
In the tilted coordinates, the extrapolation direction is potentially closer to the propagation direction.
Therefore, in tilted coordinates, we can extrapolate the wavefield accurately with a less accurate extrapolator.
Waves that were overturned in Cartesian coordinates are not overturned in tilted coordinates.
Therefore, we can image them with the one-way wave equation.

** Next:** Numerical examples
** Up:** Shan and Biondi: Plane-wave
** Previous:** Introduction
Stanford Exploration Project

4/5/2006